Is there such a thing as a 1965 1/2 Ford Mustang?

Is there such a thing as a 1965 1/2 Ford Mustang? - 1

No. You must be thinking of 64 1/2. It came out late in the year but too early to be a '65. Historically, model change-over is when factories shut-down to re-tool for a couple of weeks in August. Then production resumes and the new models start showing up at dealer lots in Sept.

Nope. The First Mustangs were called 1964 1/2 models because they were released for sale to the public in the middle of the 1964 model year. There were no 1965 1/2 models.

No, just 1964.5 but often people lump those in with 1965 too